"We have no interest in taking the company public anytime in the near future," he told CNBC in an exclusive interview. "Why should I?"

With the global taxi and limousine app in 50 cities around the world, Kalanick said, he is focused on aggressive global expansion. All you have to do is go to the Uber website to see dozens of international jobs available, from Bogota and Mexico City to Beijing and Mumbai.

Founded in 2009, the company is increasing revenue at a double-digit rate every month and recently closed another round of venture financing, he said.

Uber's most recent investors include Google Ventures and TPG Growth, which led its C Series round for $258 million. Early investors included Troy Carter, Lady Gaga's former manager; Amazon founder Jeff Bezos' Bezos Expeditions; Goldman Sachs; and Benchmark Capital. The company has raised more than $300 million to date.

While San Francisco-based Uber is growing quickly and expanding its workforce, the company also faces some hurdles.

The company has legal challenges with urban taxi and limousine agencies around the country, and is in a spat with the California Public Utilities Commission specifically. Uber would not comment on ongoing legal discussions with regulators. It also faces pricing pressure from competitors such as Lyft.